PhD student Gianluca Esposito

Quantum Resources with constraints

Quantum Resource Theory is a framework for the understanding of what is useful and costly in quantum operations and quantum information processing. In this framework, there are free operations and free states that one can generate and use at no cost. For example, in the resource theory of entanglement, LOCC operations and separable states are free. In the resource theory of stabilizer properties, stabilizer states and Clifford operations are free. These two examples are paramount for obtaining quantum advantage in quantum computation. In the presence of constraints, one is only able to access states and operations within a subspace. One therefore wonders what is the average resource in this subspace. Moreover, to understand how much the constraints have either implemented or depleted resources, one defines the notion of resource gap associated to a subspace. We study the resource gap of stabilizer entropy associated to a certain class of projectors. Our results have a large range of applications from quantum error correcting codes to gauge theories.